Material Taken From: Mathematics for the international student Mathematical Studies SL Mal Coad, Glen Whiffen, John Owen, Robert Haese, Sandra Haese and Mark Bruce Haese and Haese Publications, 2004

Consider this table: How many people are in the sample? – How many males? – How many females? This is called a 2 x 2 contingency table. Section 18D – The Χ 2 Test of Independence

Gender vs. Regular Exercise How are gender and regular exercise related?

Gender vs. Regular Exercise The variables may be dependent: – Females may be more likely to exercise regularly than males. The variables may be independent: – Gender has no effect on whether they exercise regularly. A chi-squared test is used to determine whether two variables from the same sample are independent.

How to do it: 1)Write the null hypothesis (H 0) and the alternate hypothesis (H 1 ). 2)Create contingency tables for observed and expected values. 3)Calculate the chi-square statistic and degrees of freedom. 4)Find the chi-squared critical value (booklet). Depends on the level of significance (p) and the degrees of freedom (v). 5)Determine whether or not to accept the null hypothesis.

1. Null and Alternate Hypothesis H 0 : ________ is independent of ________ H 1 : ________ is dependent on ________

2. Contingency Tables  Observed Frequencies  Expected Frequencies Column1Column2Totals Row1absum row1 Row2cdsum row2 TotalsSum column1Sum column2total Column1Column2Totals Row1sum row1 Row2sum row2 Totalssum column 1sum column 2total

3. Χ 2 Statistic On TI-84 Put observed data in Matrix A Stat> Tests > C: χ 2 -Test Calculate Output: Χ 2  Χ 2 calculated value df  degrees of freedom in Matrix B  expected values

4. Find the Critical Value Get this from the formula booklet. Significance level (p) is always given in the problem.  A 5% significance level = 95% confidence level Degrees of freedom: v = (c - 1)(r – 1) where c = number of columns in table and r = number of rows in table

5. Accept Null Hypothesis? If X 2 calc < Critical Value ACCEPT the null hypothesis If X 2 calc > Critical Value REJECT the null hypothesis Can this be determined from the p-value?

On the calculator: Put your contingency table in matrix A  STAT  TESTS  C: χ 2 Test  Observed: [A]  Expected: [B] (this is where you want to go)  Calculate

Homework Exercises from Hodder Education textbook, Pg #1, #3, #5